Crosslinked polyethylene (XLPE) is a common material for power cable insulation due to its low cost, mechanical stability, and insulating nature. It is made by converting low-density polyethylene (LDPE) to a crosslinked variant using the chemical agent dicumyl peroxide (DCP). However, the crosslinking process leaves behind byproducts that may compromise the utility of the XLPE. For example, they can contribute to space charge buildup and degradation over time. Here, the thermally stimulated depolarization current (TSDC) technique is used to analyze the susceptibility of XLPE to charge buildup and the origins of the stored charge. Comparisons to LDPE are made to determine if DCP byproducts play a role. In general, three peaks are observed in both XLPE and LDPE, with only one being observed above room temperature. That homocharge peak arises from charge injection that occurs during poling, and has greater magnitude in LDPE than in XLPE. It's magnitude in XLPE can be controlled by the applied field, but the same cannot be said for LDPE. For the two other peaks observed, one is potentially attributable to polymer motion or glass transition phenomena, while the origin of the other is currently speculated to be related to moisture content.